4.2.1.3.2 Control Basics
Tuning the position controller with cascaded structure is pretty straight forward. Cascaded controller is usually
used in PI-P form, i.e. inner loop (velocity control loop) is only using the proportional part of its PID controller
and the outer loop (position controlling loop) is only using its proportional and integral part. The other form is
P-PI form, i.e. inner loop is using proportional and integral part and outer loop uses only proportional part.
The inner velocity control loop is responsible for calculating the torque reference. As a result the integral limit
of the velocity controller should be set to the maximum torque of your torque actuator (in mNm). Moreover,
the outer position control loop is responsible for controlling the reference velocity, and consequently its
integral limit should be set to the maximum velocity of your system (in rpm).
4.2.1.3.3 Tuning Concept in Brief
For tuning the cascaded structure, we should first focus on the inner (velocity) loop. As it is the inner
controlling loop, it should be faster than the outer position loop. However, if all parameters of the outer
position controller are set to 0, the inner loop will be disconnected from the user position commands. As a
result, we can increase the k of both position and velocity controllers with a ratio of 10 (k = 10 *
k ). Once the real position started to follow the reference position, we can stop increasing the k ,
and only focus on increasing k . At this stage, we can increase (sharpen) the velocity controller as much
as possible. As a rule of thumb, increase k until you get close to the instability margin (at this margin,
you will feel a vibration effect and some acoustic noise which is caused by controller sharpness). Now, you can
reduce k to 90% of its value to increase the stability margin, and remove vibration noise.
Once the velocity controller (the inner controlling loop) is tuned, it is time to tune the position controller (the
outer controlling loop). To tune the position controller loop, we should start with the P part of its PID
controller. Increase k until the entire position control gets close to instability margin. At this state, you
will feel a vibration (or acoustic noise) which is because of too sharpened position control. At this step, reduce
k to its 90% to increase the stability margin and remove the vibration/acoustic noise.
So far, the proportional parts of both inner velocity loop and outer position loop are tuned, and we can focus
on integrator part of the outer position or inner velocity loop (depends on chosen structure of controller).
Increasing the integrator constant will remove the steady state error, but at the same time, it adds some
overshoot at step responses. As a rule of thumb, you can increase k step by step until the following two
conditions are met at the same time:
the steady-state error is eliminated in a short enough period of time
the overshoot is in its acceptable range
In the following section, the explained tuning concept is divided in separate systematic steps.
P P_velocity
P_position P_position
P_velocity
P_velocity
P_velocity
P_position
P_position
I
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